I'm a few months behind on this thread, but I just pulled a 13,000lb gooseneck trailer behind my 2022 RAM 2500 crew cab Tradesman Level 2 and gas 6.4L 4x4 truck. It was an interesting experience, especially since I've pulled the same trailer with my 2019 RAM 3500 4x4 and 6.7L HO Cummins. Both have the factory gooseneck hitch prep. My gas truck has the 3.73 axle, and according to the VIN lookup on the RAM website for towing, my rig is rated to pull 14,760lbs.
Basically, on hills of any consequence, you have the pedal to the floor. The trans will not downshift as far as it could and let the Hemi roar along near redline, but rather it settles into a gear and seems to hold between 3500-4000RPM. I was able to maintain 43mph up a steep hill. Aside from not going as fast as I would like, it was not a horrible experience. The biggest drawback was braking. The Cummins exhaust brake is the best in the business and keeps you feeling extremely confident on the long hills. I feel like this brand new 2500 Hemi truck has the worst brakes of any HD truck I've ever owned even driving empty, and that doesn't help. Long pedal travel with soft feeling brakes. The trans in Tow/Haul mode does its best to use engine compression to help, but its not remotely like a diesel exhaust brake. The solution is to turn up the trailer brake controller, and you can safely tow this amount of weight, but you will be using your brake pads up quicker no doubt. Finally, for towing on flat or relatively flat ground, the truck does just fine. Even my Cummins HO truck would feel this amount of weight and not be "fast" anywhere, it just climbed hills and descended them a lot better.